Construction of Solutions of the Hamburger–Löwner Mixed Interpolation Problem for Nevanlinna Class Functions

J. A. Alcober (), I. M. Tkachenko () and M. Urrea ()
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J. A. Alcober: Universidad Politécnica de Valencia
I. M. Tkachenko: Universidad Politécnica de Valencia
M. Urrea: Universidad Politécnica de Valencia

Chapter 2 in Integral Methods in Science and Engineering, Volume 2, 2010, pp 11-20 from Springer

Abstract: Abstract By definition, a Nevanlinna class function $$\varphi \in \Re$$ is holomorphic and has a nonnegative imaginary part in the half-plane Im z > 0. In this chapter we also consider Nevanlinna functions which belong to the subclass $$\Re_0 \subset \Re$$ such that if $$\varphi(z) \in \Re_0, \lim\nolimits_{z\to \infty} (\varphi(z)/z) = 0$$ , Im z > 0. Then, due to the Riesz–Herglotz theorem, $$\varphi(z)=\int\limits^\infty_{-\infty}\frac{d\sigma(t)}{t-z}, \quad {\rm Im} \ z>0,$$ where σ(t) is a nondecreasing function such that $$\int^\infty_{-\infty} (1+t^2)^{-1} \ d\sigma(t)

Keywords: Real Axis; Contractive Function; Moment Problem; Local Constraint; Linear Fractional Transformation (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4897-8_2

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DOI: 10.1007/978-0-8176-4897-8_2

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